A stone falls freely under gravity. It covered distances `h_1, h_2` and `h_3` in the first `5` seconds. The next `5` seconds and the next `5` seconds respectively. The relation between `h_1, h_2` and `h_3` is :

Options

A. `h_(1)=(h_(2))/(3)=(h_(2))/(5)`
B. `h_(2)=3h_(1)` and `h_(3)=3h_(2)`
C. `h_(1)=h_(2)=h_(3)`
D. `h_(1)=2h_(2)=3h_(3)`

Answer

a

Explanation

For height `h_(1)`
`S_(5)=h_(1)=0+(1)/(2)g(5)^(2)`
`h_(2)=S_(10)-S_(5)`
`h_(2)=(1)/(2)g(10)^(2)-(1)/(2)g(5)^(2)-(1)/(2)g(75)`
`h_(3)=S_(15)-S_(10)=(1)/(2)g(15)^(2)-(1)/(2)g(10)^(2)`
`=(1)/(2)g(125)`
`h_(1):h_(2):h_(3)=(1)/(2)g(25):(1)/(2)g(75):(1)/(2)g(125)=1:3:5`
`h_(1)=(h_(2))/(5)`